Geodetic data inversion based on Bayesian formulation with direct and indirect prior information

Details Geodetic data inversion based on Bayesian formulation with direct and indirect prior information Geodetic data inversion based on Bayesian formulation with direct and indirect prior information

Dec 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007geoji.171.1342m&link_type=abstract

Geophysical Journal International, Volume 171, Issue 3, pp. 1342-1351.

Astronomy and Astrophysics

Astronomy

5

Abic, Bayesian Modelling, Geodetic Data Inversion, Plate Motion, Prior Information

Scientific paper

Mechanical interaction between adjacent plates, which causes crustal deformation in plate boundary zones, is rationally represented by tangential displacement discontinuity (fault slip) at plate interfaces. Given fault slip distribution, we can compute surface displacements on the basis of elastic dislocation theory. Thus we can determine the functional form of a stochastic model to extract information about unknown fault slip distribution from observed surface displacement data. In addition to observed data we usually have prior information. For example, plate tectonics postulates that primary fault slip is parallel to relative plate motion. This is direct prior information that bounds the values of model parameters within certain ranges. From physical consideration we may impose prior constraint on the roughness of fault slip distribution. This is indirect prior information that regulates the structure of stochastic models. By combining the direct and indirect prior information with observed data in a proper way we constructed a Bayesian model for geodetic data inversion, which has a hierarchic flexible structure controlled by hyper-parameters. The optimum values of hyper-parameters are objectively determined from observed data by using Akaike's Bayesian Information Criterion (ABIC). The inversion formula derived from the Bayesian model unifies the Jackson-Matsu'ura formula with direct prior information and the Yabuki-Matsu'ura formula with indirect prior information in a rational way. We demonstrated the effectiveness of the unified inversion formula through the analysis of the surface displacement data associated with the 1923 Kanto earthquake. In the analysis with direct and indirect prior information we obtained the bimodal distribution of fault slip almost parallel to plate convergence on the North American-Philippine Sea Plate interface. If we ignore the direct prior information in the analysis, additional significant distribution of fault slip perpendicular to plate convergence appears to the east, which is incomprehensible from plate tectonics.

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